Answers
Required true statements are B, C, D, G, H, I, L, M.
What is factor?
In mathematics, factors refer to the numbers that can be multiplied together to obtain a given number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Based on the given factors, we can conclude that:
f(x) has a factor of 3, which means that 3 is a root/solution of f(x).
f(x) has a factor of (2x-1), which means that 2x-1=0 or x=1/2 is a root/solution of f(x).
f(x) has a factor of (x+5), which means that x+5=0 or x=-5 is a root/solution of f(x).
Using these facts, we can determine which statements are true:
A) -1/2 is not a root/solution of f(x). (False)
B) We can check if this expression is equivalent to f(x) by factoring it:
6x² - 33x - 15 = 3(2x² - 11x - 5) = 3(x - 5)(2x + 1).
This shows that f(x) has factors of 3, (2x-1) and (x+5), so this statement is true.
C) -5 is a root/solution of f(x). (True)
D) 3 is a root/solution of f(x). (True)
E) We can check if this expression is equivalent to f(x) by factoring it:
2x²+9x-5 = (2x - 1)(x + 5), which is not the same as the factors given for f(x), so this statement is false.
F) 0 is not necessarily a root/solution of f(x), since the factors given do not guarantee that f(x) intersects the x-axis at 0. (False)
G) We can check if this expression is equivalent to f(x) by factoring it:
6x²+27x-15 = 3(2x²+9x-5) = 3(2x-1)(x+5), which shows that f(x) has the same factors as this expression, so this statement is true.
H) 1/2 is a root/solution of f(x). (True)
I) 5 is a root/solution of f(x). (True)
J) We can check if this expression is equivalent to f(x) by factoring it:
2x²-9x-5 = (2x + 1)(x - 5), which is not the same as the factors given for f(x), so this statement is false.
K) -3 is not necessarily a root/solution of f(x), since the factors given do not guarantee that f(x) intersects the x-axis at -3. (False)
L) To find the x-intercepts of f(x), we need to set f(x) equal to zero and solve for x:
f(x) = 3(x + 5)(2x - 1) = 0
This equation has roots of x=-5 and x=1/2, which means that the x-intercepts of f(x) are (-5, 0) and (1/2, 0). So, this statement is true.
M) To find the x-intercepts of f(x), we need to set f(x) equal to zero and solve for x:
f(x) = 3(x + 5)(2x - 1) = 0
This equation has roots of x=-5 and x=1/2, which means that the x-intercepts of f(x) are (-5, 0) and (1/2, 0).
So, this statement is true.
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Related Questions
The perimeter of a rectangle is 110, and the width is 4 times
the length. What is the width?
33
O 44
O 66
O 55
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option B, 44}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Perimeter of the rectangle is 110. Width is 4 times the length}[/tex]
Find: [tex]\textsf{The width}[/tex]
Solution: So, we are given two different statements in the problem. The first one states that the perimeter of the given rectangle is 110. We know that the perimeter formula is equal to 2(length + width). Since we know that the perimeter is equal to 110 that means that we can set the perimeter formula equal to 110.
Therefore, the first equation would be [tex]\textsf{2(length + width) = 110}[/tex].
The second statement states that the width is 4 times the length. Using simple algebra we can make an equation which states that the width on one side is equal to the length multiplied by 4 on the other side.
Therefore, the second equation would be [tex]\textsf{width = 4 * length}[/tex].
Now that we have created two equations these two would be considered as a system of equations. We can now plug in the second formula into the first one and solve for the length.
[tex]\textsf{2(length + (4 * length)) = 110}[/tex][tex]\textsf{2(5 * length)) = 110}[/tex][tex]\textsf{10 * length = 110}[/tex][tex]\textsf{(10 * length)/10 = (110)/10}[/tex][tex]\textsf{length = 11}[/tex]Now that we have the length, we can plug the length into the second formula and solve for the width.
[tex]\textsf{width = 4 * length}[/tex][tex]\textsf{width = 4 * 11}[/tex][tex]\textsf{width = 44}[/tex]In conclusion, after creating two equations and forming them into a system of equations we were able to solve for the width and determine that the value of it is 44. Therefore, the option that matches our answer would be [tex]\textsf{Option B, 44}[/tex].
EASY 7TH GRADE MATH NEED DONE TODAY ( DOING THIS AGAIN BC THE LAST GUY DIDNT SHOW NO WORK)
the tens digit of a 2 digit number is 3 more than twice the units digit. if the digits are reversed, the new number is 54 less than the original number
Answers
Let's think of this number as T|U where T is the tens position digit and U is the units position digit.
Original number has value 10T+U. U=3T (first sentence).
Second sentence deals with U|T, which has value ('new number') 10U+T.
Half the new number is 21 < twice the original means:
½(10U+T) = 2(10T+U) - 21
There you have a system of two equations in two unknowns. You may now solve it.
Check the answers for reasonableness and correctness. (Also check my work producing the last equation)
Note I have used the vertical separation symbol "|" to segregate the two digits of a 2-digit number.
during the course of a motor test, the motor rpm (revolutions per minute) is measured and recorded at regular intervals as: 990 1030 950 1050 1000 980 calculate the mean value, standard deviation and the best estimate of the true value for this data set. over what interval would 50% of the entire population of motor speed values fall? test the data set for potential outliers.
Answers
The best estimate of the true value for this data set is the mean value, which is 1000 rpm.
To calculate the mean value, we add up all the values and divide by the
number of values:
(990 + 1030 + 950 + 1050 + 1000 + 980) / 6 = 1000
So the mean value is 1000 rpm.
To calculate the standard deviation, we need to first calculate the
variance:
Variance =[tex][(990 - 1000)^2 + (1030 - 1000)^2 + (950 - 1000)^2 + (1050 - 1000)^2 + (1000 - 1000)^2 + (980 - 1000)^2] / 6[/tex]
Variance = 12000 / 6 = 2000
So the variance is [tex]2000 (rpm)^2[/tex].
The standard deviation is the square root of the variance:
Standard deviation = √(2000) = 44.7 rpm
The best estimate of the true value for this data set is the mean value, which is 1000 rpm.
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if four circles are placed around a central circle, as pictured below, what is the relationship between the diameter of the outer circles and the diameter of the inner circle? explain.
Answers
This relationship shows that the diameter of the central circle (2R) is twice the diameter of each outer circle (2r).
In this configuration, four outer circles are placed around a central circle, such that they are all tangent to the central circle and tangent to each other.
To determine the relationship between the diameter of the outer circles and the diameter of the inner circle, follow these steps:
1. Let the radius of the outer circles be r and the radius of the central circle be R.
2. In this arrangement, the distance between the centers of any two adjacent outer circles is equal to the sum of their radii, which is 2r.
3. Now, draw a straight line connecting the centers of these two adjacent outer circles.
This line will pass through the center of the central circle.
4. The length of this line is the sum of the radii of the outer circle, the central circle, and another outer circle, which is
r + R + r = 2r + R.
5. Observe that the line connecting the centers of the two adjacent outer circles, along with the radii connecting the center of the central circle to the points of tangency, forms a right-angled isosceles triangle.
6. Since it is an isosceles triangle, the length of the line connecting the centers of the two adjacent outer circles (2r + R) is also the length of the other side of the triangle, which is equal to the diameter of the outer circle (2r).
7. Therefore, the relationship between the diameter of the outer circles and the diameter of the inner circle is:
2r = 2r + R.
8. Simplify the equation to find the relationship: R = 2r.
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mark is buying different nuts to make a mixed nut platter to serve at a party. he buys kilograms of peanuts, grams of almonds and dekagrams of cashews. what is the total weight in grams of the nuts he purchased? enter only the number. do not include units.
Answers
As per the given data, Mark is buying different nuts to make a mixed nut platter to serve at a party. the total weight in grams of the nuts Mark purchased is 4000.
He buys 1.5 kilograms of peanuts, 500 grams of almonds and 200 dekagrams of cashews. We need to calculate the total weight in grams of the nuts he purchased.Calculation:Total weight in grams of peanuts = 1.5 × 1000 = 1500 grams. Total weight in grams of almonds = 500 grams. Total weight in grams of cashews = 200 × 10 = 2000 grams. . Adding all the weights: Total weight = 1500 + 500 + 2000 = 4000. Therefore, the total weight in grams of the nuts Mark purchased is 4000. The gross weight is the total weight of the goods carried, including all packaging but excluding the tare weight of the transport unit. The tare weight is the weight of a transport unit before any cargo is loaded.
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Which fraction is equivalent to 0.13~
Answers
Answer: 13/100
Step-by-step explanation:
in illustration 3, 'cards' were shuffled and printed out. line 35 shuffles the deck. how many columns were used for each card in the deck?
Answers
In order to print out a deck of 52 cards, and each card having its suit and value displayed on the same line, 13 columns were used for each of the card.
In Illustration 3, assuming that the deck contains 52 cards, each card in the deck was printed using 13 columns. This is because a standard deck of playing cards contains four suits (clubs, diamonds, hearts, and spades), and each suit has 13 cards (Ace, 2-10, Jack, Queen, King).
Therefore, to print out a deck of 52 cards, with each card having its suit and value displayed on the same line, 13 columns were used for each card.
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The complete question is :
In Illustration 3, a deck of cards was shuffled and printed out. Line 35 shuffles the deck. How many columns were used for each card in the deck, assuming that the deck contains 52 cards?
The table below represents the cost that a computer repair company charges for the amount of hours that they will work to repair a computer.
Write an equation that can be used to determine the charge for a computer repair for any possible number of hours the repair takes to complete. Explain what each part of the equation represents.
Answers
The equation that can be used to determine the charge for a computer repair for any possible number of hours is y = 25x + 5, where x is the number of hours and y is the charge in dollars for a computer repair of x hours.
9. Binder's Bookstore purchases paperback novels from
Parker Publishing. The markup for each book is 56% of its
selling price. Binder's pays $5.80 for each book. What is the
selling price?
Answers
according to the question, the selling price of each book is $13.18.
Explain price?When the quantity supplied and wanted are equal, prices are in equilibrium. The quantity provided and demanded are equal at the price of equilibrium.
Let's denote the selling price of each book as "x". The markup for each book is 56% of its selling price, so the profit that Binder's Bookstore makes on each book is:
0.56x
If we add this profit to the cost of the book, we get the selling price:
x = 5.80 + 0.56x
Solving for x, we can simplify as follows:
0.44x = 5.80
x = 13.18
Therefore, the selling price of each book is $13.18.
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A basketball coach thinks that as his team progresses through the season, his players are not scoring as many points as they were in the previous weeks. He uses a table to record the number of points that his team scores for the first ten weeks of the season.
Week Game Points
1 67
2 58
3 63
4 60
5 66
6 52
7 77
8 60
9 68
10 59
Create a scatter plot to represent the data in the table. Use your scatter plot to correctly finish the statement below.
When graphed on a scatter plot, the data has
. Therefore, the basketball coach was
.
Answers
When graphed on a scatter plot, the data has a generally decreasing trend. Therefore, the basketball coach was correct in thinking that his players are not scoring as many points as they were in the previous weeks.
Based on the scatter plot, we can observe the trend that the number of game points decreases as the week progresses.
The points on the scatter plot are generally trending downwards, indicating a decrease in the number of points scored over time.
Therefore, the basketball coach was correct in his observation that his players are not scoring as many points as they were in the previous weeks.
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according to the following output from excel histogram data analysis tool, how many observations are less than or equal to 50? answer with an integer value. bin frequency cumulative % 15 4 0.94% 20 62 15.53% 25 101 39.29% 30 70 55.76% 35 83 75.29% 40 20 80.00% 45 45 90.59% 50 9 92.71% 55 27 99.06% 60 0 99.06% 65 3 99.76% 70 0 99.76% more 1 100.00%
Answers
There are 92 observations that are less than or equal to 50.
To calculate the cumulative frequency, we need to add up the frequencies of all the bins up to and including the bin in question. This can be calculated by adding up the frequency values for the bins that include values less than or equal to 50:
4 (from bin 15) + 62 (from bin 20) + 101 (from bin 25) + 70 (from bin 30) + 83 (from bin 35) + 20 (from bin 40) + 45 (from bin 45) + 9 (from bin 50) = 394
So, the cumulative percentage for the bin containing 50 is 92.71%. Therefore, the number of observations less than or equal to 50 is approximately 92.
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Show your work
What is the area of the composite figure?
Answers
Step-by-step explanation:
different to the suggested graphic representation, which goes wild with several complex sub-figures, I see simply a rectangle (2×9 × 4) at the bottom and a triangle standing on top of it (2×(9-6) × (16-4)).
the area of the rectangle is
2×9 × 4 = 18×4 = 72 ft²
the area of the triangle (remember : baseline × height / 2) is
2×(9-6) × (16-4) / 2 = 2×3 × 12 / 2 = 3×12 = 36 ft²
the total area is then
72 + 36 = 108 ft²
Can someone PLEASE help me ASAP it’s due today!! I will give brainliest if it’s all done correctly.
Answer part A, B, and C for brainliest!!
Answers
The experimental probabilities have their values to be P(3) = 1/12, P(6) = 1/4 and P(Less than 4) = 1/2
Evaluating the experimental probabilitiesExperimental probability of 3
From the table of values, we have
n(3) = 1
Total = 12
So, we have
P(3) = 1/12
Experimental probability of 6
From the table of values, we have
n(6) = 3
Total = 12
So, we have
P(6) = 3/12
P(6) = 1/4
Experimental probability of less than 4
From the table of values, we have
n(Less than 4) = 6
Total = 12
So, we have
P(Less than 4) = 6/12
P(Less than 4) = 1/2
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what word are you reminded of when you hear the word radian? discuss this with your team and make a conjecture about how this might relate to a way to measure angles. be prepared to share your ideas with the class.
Answers
Radians are a unit of measurement for angles used in mathematics and physics. They are defined as the ratio between the length of an arc of a circle and the radius of that circle.
One of the most important benefits of using radians to measure angles is that they simplify calculations involving angles, making them easier to work with.
Additionally, they allow for a more elegant and unified approach to mathematical and physical problems involving angles. So, in short, the word "radian" might be associated with concepts such as circles, arcs, and the measurement of angles in mathematics and physics.
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In Stamford, the library is 7 kilometers south of the courthouse and 4 kilometers west of the community swimming pool. If a bird flew directly from the courthouse to the library, then from the library to the swimming pool, and then from the swimming pool back to the courthouse, what would be the total distance flown? If necessary, round to the nearest tenth.
Answers
AB = sqrt((7 km)^2 + (4 km)^2) ≈ 8.1 km
BC = 7 km
CA = sqrt((7 km)^2 + (4 km)^2) ≈ 8.1 km
The total distance flown would be the sum of these distances:
AB + BC + CA ≈ 8.1 km + 7 km + 8.1 km ≈ 23.2 km
Therefore, the bird would have flown approximately 23.2 kilometers in total.
PLEASE HELP! WILL TRY AND DO BRAINLYEST! INCLUDE SCRATCH AND CORRECT ANSWER. THANK YOU!
Answers
From the given coordinates geometry function will be y=-3x+1.
What is linear equation?Plotting points on a coordinate plane will provide the graph of the function y = -3x + 1. To accomplish this, we can select various x values, enter them into the equation, and then solve for y. As an illustration, if x = 0, then y = -3(0) + 1 = 1. We now get the graph's point (0, 1) thanks to this. Similar to the previous case, if we select x = 1, then y = -3(1) + 1 = -2. This results in the graph's point (1, -2) for us. By repeating this procedure, we can identify more points, which we can then join with a straight line to create the function's graph. A straight line with a slope of -3 and the point appears on the graph as a result (0, 1).
from graph we can write coordinates ,
(-1,4),(0,1),(1,-2),(2,-5)
so from these coordinates ,function will be
y=-3x+1.
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if twice a number is equal to that number minus five, what is three times that number plus seventeen minus that number?
Answers
The value of three times the number plus 17 - that same number is found to be 7.
It is provided that if twice a number is equal to that number minus then we have to find what is three times that number plus 17 minus that number.
Let's say that the number we are talking about his x.
From the given condition we can write at the twice of x will equal to x minus x - 5.
2x = x-5
Solving this simple algebraic equation.
x = -5.
Now, to find the answer,
3x + 17 - x
Putting values,
= 3(-5) + 17 -(-5)
= -15 + 17 + 5
= 7.
So, the value of thrice the number added to number minus from 17 is 7.
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may I get help please
Answers
Answer:
5
Step-by-step explanation:
8.MP.3 Critique Reasoning Craig says
that this number line shows. Do you
agree with Craig? Explain why or why not.
Answers
Craig is accurate in that the supplied number line reflects the value of 1/3 since in the situation at hand, the red dot represents the value of 1/3.
What is critique reasoning?
Once someone outlines their solution and how they approached the challenge, clarifying questions should be asked.
List the parallels and differences between several approaches to solving the issue.
Find the mistake in a wrong response, and then provide proof to support your claim.
Create strong arguments and evaluate other people's reasoning.
What It Means: When kids can give us the right answer and explain how they arrived at it, we know they fully understand a topic.
So, in the given situation the red dot represents the value of 1/3, and thus Craig is correct that the given number line represents the value of 1/3.
Therefore, Craig is accurate in that the supplied number line reflects the value of 1/3 since in the situation at hand, the red dot represents the value of 1/3.
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In ΔPQR, m ∠ � = ( � + 13 ) ∘ m∠P=(x+13) ∘ , m ∠ � = ( 10 � + 13 ) ∘ m∠Q=(10x+13) ∘ , and m ∠ � = ( 2 � − 2 ) ∘ m∠R=(2x−2) ∘ . Find m ∠ � . m∠Q.
Answers
However, this answer does not make sense, as angles in a triangle cannot be negative. This means that there is no solution to this problem .
To solve this problem, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Let's first find the measure of angle P:
m∠P + m∠Q + m∠R = 180
Substituting in the given measures:
(x + 13) + (10x + 13) + (2x - 2) = 180
Simplifying and solving for x:
13x + 24 = 180
13x = 156
x = 12
So m∠P = (x + 13) = 25 degrees.
Next, we can use the fact that the angles opposite equal sides in a triangle are congruent. Since we know that PR and QR are equal, we have:
m∠P = m∠R
So m∠R = 25 degrees.
Finally, we can find m∠Q:
m∠Q = m∠P + m∠R - 180
Substituting in the values we found:
m∠Q = 25 + 25 - 180 = -130
However, this answer does not make sense, as angles in a triangle cannot be negative. This means that there is no solution to this problem.
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suppose you take a multiple choice test of 100 questions. each question has 5 possible answers (only one of which is correct) and you select one answer for each question randomly. what is the standard deviation of the number of questions you get correct?
Answers
Answer:
20
Step-by-step explanation:
So there is a total of 1/5 chance of getting an answer right, because there are 5 possibilities and only 1 is correct.
Now because there are 100 Questions, we will multiply our probability with the total value (in this case its a 100).
So 1/5 = .2
.2 × 100 = 20
The standard deviation of the number of questions answered correctly is 4. This means that on average, the number of questions answered correctly will be within 4 of the expected value.
The standard deviation of the number of questions answered correctly in a multiple-choice test of 100 questions with 5 possible answers for each question, assuming random selection of one answer per question, can be calculated using the formula for the binomial distribution, which is the square root of n times p times q, where n is the total number of trials, p is the probability of success on each trial, and q is the probability of failure on each trial.
Using the formula for the binomial distribution, the standard deviation of the number of questions answered correctly can be calculated as follows:
n = 100 (total number of trials)
p = 1/5 (probability of success on each trial, i.e., selecting the correct answer)
q = 4/5 (probability of failure on each trial, i.e., selecting one of the incorrect answers)
Therefore, the standard deviation is:
√(100 x 1/5 x 4/5) = √16 = 4
Therefore, the standard deviation of the number of questions answered correctly is 4. This means that on average, the number of questions answered correctly will be within 4 of the expected value.
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Write a quadratic function in standard form that models the table.
Answers
Answer:
3=0
Step-by-step explanation:
please help me i dont understand this
Answers
Answer:
diameter = 2× radius
circumference = [tex]2\pi r[/tex]
Area = [tex]\pi r^{2}[/tex]
use this formulas and put the given values and you will get the answers
Step-by-step explanation:
Use the given measurements to solve the triangle. Round lengths of sides to the
nearest tenth and angle measures to the nearest degree.
a = 500, b = 300
The measure of angle B is approximately
(Round to the nearest degree.)
Answers
To find the measure of angle B, we can use the inverse tangent function:
tan(B) = opposite / adjacent = a / b
tan(B) = 500 / 300
B = arctan(500 / 300)
B ≈ 59.0 degrees
Therefore, the measure of angle B is approximately 59 degrees (rounded to the nearest degree).
6. Find the value of the following investment using compound interest.
(i) GH 18000.00 for 3 years at 10% per annum.
(ii)GH 80000.00 for 10 years at 15 per annum
Answers
Answer:
Step-by-step explanation:
How many liters of a 30% NaCl solution should be mixed with 1 L of a solution that contains no NaCl to obtain a 24% NaCl solution?
Answers
Answer: 125
Step-by-step explanation:
Members of the student government are planning a movie night on campus. They have asked a random sample of students which of four movies the students would prefer. Here are the results.
There are 800 students total on campus.
Based on the above information, how many students on campus would we expect to prefer Movie B?
Round your answer to the nearest whole number. Do not round any intermediate calculations.
Answers
The nearest whole number, we get that we can expect about 419 students on campus to prefer Movie B.
How to calculate addition?
Addition is a basic arithmetic operation that involves combining two or more numbers to obtain their sum. Here's how to calculate addition:
Write the numbers to be added one below the other, aligning the digits according to their place value (ones below ones, tens below tens, and so on).
Start by adding the digits in the ones column (the rightmost column). If the sum is less than 10, write it down below the line. If the sum is 10 or greater, carry the 1 to the next column (the tens column).
Move to the next column (the tens column) and add the digits in that column, along with any carried-over 1 from the previous column. Again, if the sum is less than 10, write it down below the line. If the sum is 10 or greater, carry the 1 to the next column (the hundreds column).
Repeat this process for each column, working from right to left, until you have added all the numbers.
The final result is the sum of the numbers.
We can use the proportion of students in the sample who preferred Movie B to estimate the expected number of students on campus who would prefer Movie B.
The proportion of students in the sample who preferred Movie B is:
Proportion of students who prefer Movie B in the sample = Number of students who prefer Movie B in the sample / Sample size
= 66 / (39 + 66 + 2 + 25)
= 0.524
So, we can expect that approximately 0.524 * 800 = 419.2 students on campus would prefer Movie B.
Rounding this to the nearest whole number, we get that we can expect about 419 students on campus to prefer Movie B.
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PLS HELP ME OUT W THIS MATH QUESTION RQ
Answers
Step-by-step explanation:
4x^2 + 16x -4 factor out a '4'
4 ( x^2 + 4x -1) Done.
There isn't anything else you can factor out of the three terms
cuanto vale x? urgente
Answers
Answer:
x = 15°
Step-by-step explanation:
We Know
(2x + 45) + x = 90°
Let's solve
2x + 45 + x = 90°
3x + 45 = 90°
3x = 45°
x = 15°
the level of significance is the group of answer choices same as the confidence coefficient. maximum allowable probability of type i error. same as the p-value. maximum allowable probability of type ii error.
Answers
The level of significance in a hypothesis test is the maximum allowable probability of a Type I error. A Type I error occurs when you reject a null hypothesis that is actually true.
The level of significance is usually denoted by the symbol α (alpha) and is expressed as a percentage or a decimal value, such as 5% or 0.05. This means that if the level of significance is set at 5%, there is a 5% chance of making a Type I error when the null hypothesis is true.
To answer the student question, the level of significance is not the same as the confidence coefficient or the p-value. The confidence coefficient is related to the confidence interval, which is a range of values within which the true population parameter is likely to fall. The confidence coefficient (1 - α) represents the probability that the true population parameter lies within the confidence interval.
The p-value, on the other hand, is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. If the p-value is less than or equal to the level of significance, you reject the null hypothesis and accept the alternative hypothesis.
Lastly, the maximum allowable probability of a Type II error (denoted by β) is not the same as the level of significance. A Type II error occurs when you fail to reject a null hypothesis that is actually false. The power of a test is defined as (1 - β) and represents the probability of correctly rejecting a false null hypothesis.
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